5 The time taken for a particular train journey is normally distributed. In the past, the time had mean 2.4 hours and standard deviation 0.3 hours. A new timetable is introduced and on 30 randomly chosen occasions the time for this journey is measured. The mean time for these 30 occasions is found to be 2.3 hours.

1. Stating any assumption(s), test, at the \(5 \%\) significance level, whether the mean time for this journey has changed.
2. A similar test at the \(5 \%\) significance level was carried out using the times from another randomly chosen 30 occasions.
   (a) State the probability of a Type I error.
   (b) State what is meant by a Type II error in this context.